If you're already on the iOS 6.1 beta, you can upgrade on-device and over-the-air (OTA) by going to Settings > General > Software update. Otherwise you can, as always, download the beta from developer.apple.com

I was surprised to see iOS 6 supported the iPhone 3GS considering the fact that iPhone 3G couldn't use iOS5. But from the content of this article it seems like iOS 6.0.1 will be the last iOS version for the iPhone 3GS (?)

I have a Verizon iPhone 5 with iOS 6.0.1. I've restarted, restored, reset network settings, and forgot and signed back into my wifi and my phone still has a problem where while I am using safari, my phone will lose connection to the wifi. I have to go to settings>wifi and turn it off and back on for my phone to reconnect. If anyone has any ideas to fix this I'd really appreciate it.